- #1
find_the_fun
- 148
- 0
For megre sort alogirthm the runtime is T(n)=nb+cnlog(n). It's not quite clear to me why this is O(nlogn) is it because b and c are constants?
find_the_fun said:For megre sort alogirthm the runtime is T(n)=nb+cnlog(n). It's not quite clear to me why this is O(nlogn) is it because b and c are constants?
O(nlogn) is a way of measuring the time complexity of an algorithm, specifically how it scales with the input size. It indicates that the runtime of the algorithm grows at a rate proportional to n multiplied by log n. Merge Sort has a time complexity of O(nlogn) because it consistently divides the input into smaller halves and then merges them in a sorted manner.
Merge Sort is considered a "divide and conquer" algorithm because it divides the input into smaller subproblems, solves each subproblem independently, and then combines the solutions to solve the original problem. In the case of Merge Sort, the input is divided into smaller halves until they are sorted, and then the sorted halves are merged together to produce a fully sorted list.
The best case scenario for Merge Sort's runtime is when the input is already sorted. In this case, the algorithm still divides the input into smaller halves, but the merge step simply combines the already sorted halves without needing to perform any additional comparisons. This results in a runtime of O(nlogn).
The worst case scenario for Merge Sort's runtime is when the input is in reverse sorted order. In this case, the algorithm must perform the maximum number of comparisons at each level of recursion, resulting in a runtime of O(nlogn). This is because the algorithm still needs to divide the input into smaller halves and then merge them in a sorted manner.
In general, Merge Sort has a better time complexity than other popular sorting algorithms like Bubble Sort, Selection Sort, and Insertion Sort. This is because it consistently divides the input into smaller halves, resulting in a runtime of O(nlogn). This makes Merge Sort more efficient for larger input sizes, although it may require more memory due to its use of temporary arrays.